Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3186 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#17981 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C42 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C11×#3169 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
726 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,17)(14,16,19,18)(20,21,24,28,25,22,29,27)(23,26,31,34,32,30,35,33);(13,16)(14,19)(17,18)(20,22)(21,25)(23,30)(24,27)(26,32)(28,29)(31,33)(34,35);(13,17)(16,18)(20,23,29,35,25,32,24,31)(21,26,27,33,22,30,28,34);(21,22)(26,30)(27,28)(33,34)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 10969);